It isn’t just that workers are cheaper abroad. Rather, Apple’s executives believe the vast scale of overseas factories as well as the flexibility, diligence and industrial skills of foreign workers have so outpaced their American counterparts that “Made in the U.S.A.” is no longer a viable option for most Apple products.

Last year, Apple earned over $400,000 in profit per employee, more than Goldman Sachs, Exxon Mobil or Google.

However, what has vexed Mr. Obama as well as economists and policy makers is that Apple — and many of its high-technology peers — are not nearly as avid in creating American jobs as other famous companies were in their heydays.

Apple employs 43,000 people in the United States and 20,000 overseas, a small fraction of the over 400,000 American workers at General Motors in the 1950s, or the hundreds of thousands at General Electric in the 1980s. Many more people work for Apple’s contractors: an additional 700,000 people engineer, build and assemble iPads, iPhones and Apple’s other products. But almost none of them work in the United States. Instead, they work for foreign companies in Asia, Europe and elsewhere, at factories that almost all electronics designers rely upon to build their wares.

Apple executives say that going overseas, at this point, is their only option. One former executive described how the company relied upon a Chinese factory to revamp iPhone manufacturing just weeks before the device was due on shelves. Apple had redesigned the iPhone’s screen at the last minute, forcing an assembly line overhaul. New screens began arriving at the plant near midnight.

A foreman immediately roused 8,000 workers inside the company’s dormitories, according to the executive. Each employee was given a biscuit and a cup of tea, guided to a workstation and within half an hour started a 12-hour shift fitting glass screens into beveled frames. Within 96 hours, the plant was producing over 10,000 iPhones a day.

“The speed and flexibility is breathtaking,” the executive said. “There’s no American plant that can match that.”

For Mr. Cook, the focus on Asia “came down to two things,” said one former high-ranking Apple executive. Factories in Asia “can scale up and down faster” and “Asian supply chains have surpassed what’s in the U.S.” The result is that “we can’t compete at this point,” the executive said.

The impact of such advantages became obvious as soon as Mr. Jobs demanded glass screens in 2007.

For years, cellphone makers had avoided using glass because it required precision in cutting and grinding that was extremely difficult to achieve. Apple had already selected an American company, Corning Inc., to manufacture large panes of strengthened glass. But figuring out how to cut those panes into millions of iPhone screens required finding an empty cutting plant, hundreds of pieces of glass to use in experiments and an army of midlevel engineers. It would cost a fortune simply to prepare.

Then a bid for the work arrived from a Chinese factory.

When an Apple team visited, the Chinese plant’s owners were already constructing a new wing. “This is in case you give us the contract,” the manager said, according to a former Apple executive. The Chinese government had agreed to underwrite costs for numerous industries, and those subsidies had trickled down to the glass-cutting factory. It had a warehouse filled with glass samples available to Apple, free of charge. The owners made engineers available at almost no cost. They had built on-site dormitories so employees would be available 24 hours a day.

The Chinese plant got the job.

“The entire supply chain is in China now,” said another former high-ranking Apple executive. “You need a thousand rubber gaskets? That’s the factory next door. You need a million screws? That factory is a block away. You need that screw made a little bit different? It will take three hours.”

Another critical advantage for Apple was that China provided engineers at a scale the United States could not match. Apple’s executives had estimated that about 8,700 industrial engineers were needed to oversee and guide the 200,000 assembly-line workers eventually involved in manufacturing iPhones. The company’s analysts had forecast it would take as long as nine months to find that many qualified engineers in the United States.

In China, it took 15 days.

“I’m not worried about the country’s long-term future,” Mr. Jobs told Mr. Obama, according to one observer. “This country is insanely great. What I’m worried about is that we don’t talk enough about solutions.”